A027344 Number of partitions of n that do not contain 10 as a part.

1, 1, 2, 3, 5, 7, 11, 15, 22, 30, 41, 55, 75, 98, 130, 169, 220, 282, 363, 460, 585, 736, 925, 1154, 1440, 1782, 2205, 2713, 3333, 4075, 4977, 6050, 7347, 8888, 10735, 12925, 15541, 18627, 22297, 26620, 31734, 37741, 44825, 53118, 62865

Offset: 0

Author

Clark Kimberling

Keywords

• nonn

Crossrefs

10th column of A175788. Cf. A000041, A027336, A027337-A027343.

Programs

Maple

A41:= n-> `if`(n<0, 0, combinat[numbpart](n)):
a:= n-> A41(n) -A41(n-10):
seq(a(n), n=0..50);

Formula

G.f.: (1-x^10) Product_{m>0} 1/(1-x^m).

a(n) = A000041(n)-A000041(n-10).

a(n) ~ 5*Pi * exp(sqrt(2*n/3)*Pi) / (6*sqrt(2)*n^(3/2)) * (1 - (3*sqrt(3/2)/Pi + Pi/(24*sqrt(6)) + 10*Pi/(2*sqrt(6)))/sqrt(n) + (121/8 + 9/(2*Pi^2) + 19441*Pi^2/6912)/n). - Vaclav Kotesovec, Nov 04 2016

Extensions

More terms from Benoit Cloitre, Dec 10 2002

Edited by Alois P. Heinz, Dec 04 2010